Karim Adiprasito, June Huh, and Eric Katz. "Hodge theory for combinatorial geometries". In: arXiv preprint arXiv:1511.02888 (2015).K. Adiprasito, J. Huh and E. Katz, Hodge theory for combinatorial geometries, arXiv:1511.02888.Karim Adiprasito, June Huh, and Eric Katz, Hodge theory ...
I will tell two interrelated stories illustrating fruitful interactions between combinatorics and Hodge theory. The rst is that of Lorentzian polynomials, based on my joint work with Petter Brndén. They link continuous convex analysis and discrete convex analysis via tropical geometry, and they reveal...
Historical note. In the 20th century the physical and biological sciences have been revolutionized in probabilistic terms. Mathematicians began to look at differential equations, number theory and combinatorics in that light too. The applications expanded, among other areas, to financial mathematics and ...
1.2 together with some new combinatorics. in particular, in sect. 5.2 , using the theory of valuations of polytopes (see, e.g., [ 45 ]), we present a new proof of a formula of danilov–khovanskiĭ [ 20 , section 4] for the \(\chi _y\) -characteristic of \(x^\circ ...
The combinatorics and topology of proper toric maps We use this and the computation of Hodge- Deligne polynomials for fibers of toric fibration to give the formula for the Betti numbers of such fibers in... MA De Cataldo,L Migliorini,M Musta?? - 《Journal Für Die Reine Und Angewandte ...
In [7], we had given a monoid theoretic generalization of this phenomenon. On the way, we had applied the Putcha-Renner theory of linear algebraic monoids over algebraically closed fields to study G(F) by generalizing various results for linear algebraic groups over F such as the Iwasawa, ...
Advances in MathematicsKaz09. Kazarian M.: KP hierarchy for Hodge integrals. Adv. Math. 221 (1), 1–21 (2009) MATH MathSciNetKazarian M.: KP hierarchy for Hodge integrals. Adv. Math. 221 , 1–21 (2009) MATH MathSciNetKazarian, M. (2009) KP hierarchy for Hodge integrals. Adv. ...
In several contexts this "package" yields important results about geometry, representation theory, or combinatorics. We discuss the above properties purely in terms of linear algebra, so that some of the techniques and intuition from geometry can be brought to bear on more general problems. Our ...
In the very particular case of convenient and nondegenerate Laurent polynomials, we show (using the Brieskorn lattice and the V -filtration) that the previous results agree with the classical ones in combinatorics and we emphasize various combinatorial properties of Sabbah's Hodge numbers: on the ...